Does the Pauli exclusion principle apply to one fermion and one antifermion?

As you stated, no two fermions or anti-fermions can occupy the same state. And here by "state" we mean all quantum numbers defining the properties of our particle. So since electric charge for e.g. electron and positron are different, they can be in the same state.

Pauli exclusion principle holds for identical particles. With that in mind, one fermion and one anti-fermion can be in the same state (if that particular fermion is not its own antiparticle).